Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

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• 作者：Yongxia Zhao ; Rongming Wang ; Dingjun Yao…
• 关键词：Dividend ; Capital injection ; Dual model ; Scale function ; 60G51 ; 93E20
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：167
• 期：1
• 页码：272-295
• 全文大小：681 KB
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• 作者单位：Yongxia Zhao (1)
  Rongming Wang (2)
  Dingjun Yao (3)
  Ping Chen (4)
  
  1. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China
  2. School of Finance and Statistics, East China Normal University, Shanghai, China
  3. School of Finance, Nanjing University of Finance and Economics, Nanjing, China
  4. Faculty of Business and Economics, University of Melbourne, Melbourne, Australia
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

This paper investigates an optimal dividend and capital injection problem in the dual model with a random horizon. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends and the penalized discounted capital injections during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. By the fluctuation theory of Lévy processes, the optimal dividend and capital injection strategy is obtained. We also find that the optimal return function can be expressed in terms of the scale functions of Lévy processes. Besides, numerical examples are studied to illustrate our results. Keywords Dividend Capital injection Dual model Scale function